It doesn't need to say anything about file headers. A source file is a copyrightable work. The copyright notice and license file in that source file provide the copyright notice for that work and it's licensing terms. The MIT license, under which the work is licensed, requires the copyright notice of the work to be preserved. By removing and replacing the notice on the work, and distributing it without preserving the original notice as required by the license on the work, the license is violated.

The fact that the work is also included in a compilation, which is a separate copyright protected work, and that work has its own copyright notice and is offered under the same license, does not somehow alter the license requirements on the component work within the compilation, so that of the compilation’s copyright is preserved as required by the license of the compilation, there is no obligation to preserve the copyright notice of the component work as required by the license on the component.